CUET UG 2025 — Mathematics Calculus

2025mcqmedium

If $x = e^t$ and $y = e^{2t}$ then $\frac{d^2y}{dx^2} =$

Official previous-year question

Held on 22 May 2025 · Verified 13 Jul 2026.

Options

A
$2x$
B
$2y$
C
$2$
D
$\frac{1}{2x}$

Did you get this right?

Solution

Given $x = e^t$ and $y = e^{2t}$ .

Since $x = e^t$ , we have:

$t = \ln(x)$

Substituting into the expression for $y$ :

$y = e^{2t}$

$y = e^{2\ln(x)}$

$y = e^{\ln(x^2)}$

$y = x^2$

Taking the first derivative with respect to $x$ :

$\frac{dy}{dx} = 2x$

Taking the second derivative with respect to $x$ :

$\frac{d^2y}{dx^2} = \frac{d}{dx}(2x)$

$\frac{d^2y}{dx^2} = 2$

Therefore, $\frac{d^2y}{dx^2} = 2$

Your note

CUET UG Calculus in other years

Calculus 2026 Calculus 2024 Calculus 2023 Calculus 2022

Keep practicing Calculus

Work through every CUET UG Calculus PYQ, year by year.

Browse all Mathematics topics

Solution

Given $x = e^t$ and $y = e^{2t}$ .

Since $x = e^t$ , we have:

$t = \ln(x)$

Substituting into the expression for $y$ :

$y = e^{2t}$

$y = e^{2\ln(x)}$

$y = e^{\ln(x^2)}$

$y = x^2$

Taking the first derivative with respect to $x$ :

$\frac{dy}{dx} = 2x$

Taking the second derivative with respect to $x$ :

$\frac{d^2y}{dx^2} = \frac{d}{dx}(2x)$

$\frac{d^2y}{dx^2} = 2$

Therefore, $\frac{d^2y}{dx^2} = 2$

CUET UG 2025 — Mathematics Calculus

Options

Did you get this right?

Solution

Your note

CUET UG Calculus in other years

More CUET UG Calculus questions

Other Mathematics topics for CUET UG

Algebra

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Calculus

CUET UG 2025 — Mathematics Calculus

Options

Did you get this right?

Solution

Your note

CUET UG Calculus in other years

More CUET UG Calculus questions

Other Mathematics topics for CUET UG

Algebra

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Calculus